Analysis of a three-component model phase diagram by catastrophe theory: Potentials with two order parameters

Abstract

In this work we classify the singularities obtained from the Gibbs potential of a lattice gas model with three components, two order parameters, and five control parameters applying the general theorems provided by catastrophe theory. In particular, we clearly establish the existence of Landau potentials in two variables or, in other words, corank-2 canonical forms that are associated with the hyperbolic umbilic, ${D}_{+4},$ its dual the elliptic umbilic, ${D}_{\ensuremath{-}4},$ and the parabolic umbilic ${D}_{5}$ catastrophes. The transversality of the potential with two order parameters is explicitly shown for each case. Thus we complete the catastrophe-theory analysis of the three-component lattice model, initiated in a previous paper [Phys. Rev. B 57, 13 527 (1998)].